math-help

[obsidian oracle]

From the explanation by you, the answer provided by teacher totally wrong right? cuz the U that i circled one haven't combine with F' one U

because of this question i lose my A+ ._.

[ember kernel]

Well I don't have the whole context here, and I can't rule out the possibility that you misunderstood some part of your teacher's answer

[obsidian oracle]

oh ya sorry, do you mind i upload this whole question ?

[ember kernel]

Also, you only circled a U, not a whole path, so I can't know which of P(U|F) and P(U intersect F) you're talking about, but anyway that can't be P(U)

[ember kernel]

Do so, but in a thread then to avoid flooding this channel

[obsidian oracle]

thank you so much againnnn it's mean a lot to me

wait a moment

[ember kernel]

Hold on a second

[obsidian oracle]

this one is question 2c, one of the part of solution

[ember kernel]

probability question

[kindred pawn]

polska gurom🇵🇱

[finite nymph]

Hello, can you help me in the second question please? (I don't know what do I need to prove reciprocally)

[left knoll]

how do i prove that function is decreasing without graphing

or is graphing the only way

oh wait i can use dy/dx lmao

[earnest turret]

sorry, can anyone help me to do this que

[supple island]

solve for y when x=1 and x=2

[left knoll]

Just use wolfram alpha or something

[supple island]

write it as x²/(x-1)(x+1)² then do partial fraction decomposition

you should get 3 pretty easy integrals

[earnest turret]

ohh okayy, thank youuu!!!

[supple island]

np

[earnest turret]

hi, how about this. can anyone help me to this

[supple island]

try to multiply by t+sqrt(1-t²)/t+sqrt(1-t²)

[raw tartan]

Hi

What is 5/0

I'm confused

[supple island]

you can't divide by 0

[raw tartan]

Whyy

[supple island]

well when you divide a by b you're asking yourself:"how many times do i have to sum b by itself to obtain a?" which is also"what's the number that if multiplied by b gives a?".
try to answer both questions if b=0
@raw tartan

[zinc scroll]

it's a rule so you don't break maths

[zinc scroll]

do what PhysStudent said then sub: t = tan θ, dt = sec^2 (θ) dθ

[supple island]

i mean

why thou

also dt=dtheta/sec²

if you do what i said you end up with the integral of -t-sqrt(1-t²)

if you really wanna do a substitution you can just say that for the second one t=cos or sin

[zinc scroll]

yeah nvm i did the math wrong and somehow end up with sqrt(1+t^2), damn redoing this problem i really eff'd up rationalising the quotient soz soz

[zinc scroll]

i double checked and dt = sec²θdθ for t = tan θ from the derivative of y = tan(x). It's not relevant to the questioned cause i eff'd it but this part isn't wrong

[supple island]

right, got a bit confused

[zinc scroll]

yeah normally it's theta = f(t) no the other way around

[finite nymph]

but this is just "=>" and I am resolving an equation so I need also to prove something reciprocally ("<=")

[left knoll]

Can someone explain me why isn’t by f‘ 2x/x^4? Why is there 2x/x^2

[surreal hill]

Why would it be x^4 when (lnX)' = 1/x not 1/x^2

[left knoll]

Cause I thought If you are doing f‘ you have to do the number under line ^2 @surreal hill

[surreal hill]

happens to the best of us,hope u get it now

[wide sinew]

Can anyone help me?

[earnest turret]

okayyy, thank youuu^^

[ember kernel]

Haven't really computed integrals in a while (the further you progress into engineering courses, the less math you do I guess lol), but since it's a multiple choice question, you can always differentiate all the answers, and see which gets you to the expression in the integral

[delicate cave]

why is the value of this integral always = 2
irrespective of values of R and r
for all 0 <= r <= R & R > 0
(https://www.desmos.com/calculator/cjutsj5xf9)

[restive wedge]

can someone help me on this? what I already know is we will integrate velocity formula to get the displacement formula, and then use the displacement formula to find displacement at t=0, t=6. can we use displacement formula when speed is constant during t=6 to 12?

answer is 522. my textbook has really weird solution which I only understood up till t=6 seconds. After that they used basic distance formula for t=6 to t=12 and then a different basic displacement formula for the deceleration part. Why can't I use integrated displacement formula for all times? is there a limitation of where you can use integrated formulas ?Thanks for helping

BTW tried using integrated displacement formula ffor t=12 but the answer is coming off wrong

pls help 😭

[supple island]

have you tried solving the integral?

it's quite easy, just subsitute cosx=u

[supple island]

i mean you can always integrate, actually you are always integrating even when you say d=v* t, it's just that for t=6 to t=12 it travels at constant speed and after that it has a constant acceleration so you just have v=a* t

we are always integrating but with 3 different formulas for velocity

[restive wedge]

why can't we use the displacement formula for the distance at t=12? why is it giving me an incorrect answer? @supple island

[night kindle]

Can someone help me pls

I forgot the solution

[ripe heron]

x^2 +1 = t

derivative => 2xdx = dt

Answer is 4

[supple island]

sorry, just seen this, didn't get the notification.
not really sure what you're asking, can you post a picture of what you're tring to do?

[restive wedge]

I'm trying to use this formula of displacement to find total distance but the answer is coming off wrong

[supple island]

this is true from t=0 to t=6

from t=6 to t=12 the speed remains the same

so the formula is different

from t=6 to t=12 you have v=36

so you got s=integral from 6 to 12 of v in dt, which is 36t calcluated from 6 to 12

after that you have constant acceleration, so v=integral of a in dt a=-4m/s², we know that v=36 at the start of deceleration so it takes 9 seconds to stop

now do the integral from t=12 to t=21 of vdt to find the 3rd s

and here you go

@restive wedge

don't mind the y things above

[restive wedge]

so we can't use integrated displacement formula when speed is same?

[supple island]

you can always use the integral

[supple island]

as you can see here

[restive wedge]

no I mean the formula given in question

[supple island]

v=12t-t²?

[restive wedge]

its integral which is 6t^2-t^3/3

[supple island]

that's correct

but after t=6 the speed changes

so you have to integrate with the new formula of v

you can't use the same thing

[restive wedge]

oh so when speed changes it is no longer applicable?

ok ok

[supple island]

it is applicable you just have to do another integral

[restive wedge]

THANK YOU, you are so cool

[supple island]

also it's when speed changes its description, not just "when it changes" to be more precise

[restive wedge]

description means? meaning when speed goes from accelerating/decelerating to being constant and vice versa?

[supple island]

yeah, because from t=0 to t=6 v is described by v=12t-t², from 6 to 12 it's described by v=36 and from 12 to 21 by v=36-4t

[restive wedge]

Thank you!

[supple island]

np

[high wigeon]

hello there guys

just needed a bit of help with my homework

if anybody could help me out

[supple island]

just ask

someone will answer

[high wigeon]

i really cant seem to able to figure this question out

im using the inifinite series sum formula

but getting the wrong answer

[supple island]

doesn't work and even if it did, it qould be quite rude to tag 7k+ people for this

[high wigeon]

i apologise

[undone oxide]

well more than 7k ahah

[high wigeon]

welp

i deleted it

so hopefully

[undone oxide]

don't worry nobody has been tagged, only mods could do that

[high wigeon]

do any of you know how to solve the question tho?

[undone oxide]

sorry i haven't done maths is years :/

[high wigeon]

dw

its due this tuesday, just want to get it out of the way

[weak mortar]

bro i think your series doesn't even converge tbh

[supple island]

the series does converge

[supple island]

you can write this as ((e/pi)^n * 1/e)², we can put the 1/e² aside and see that this is a geometric series, also e/pi<1 so it converges

now you can write the series as a(1-r^n)/(1-r) where a is the first term and r is the common ratio, a=1/e² and you'll easily find that r=(e/pi)², now since r<1, we'll have that the series= 1/(e²(1-(e/pi)²)

[crisp pagoda]

can someone help me with a linear algebra's problem?

[supple island]

just ask, someone will answer

[crisp pagoda]

S = {(i,0),(0,i)};

is S a generator for the vectorial space V = C^2?

[supple island]

the dimension of C² =4

so no

you need something like (1,0)(i,0)(0,1)(0,i)

[crisp pagoda]

that's what i thought but are you able to prove it without talking about dimension? I tried: (a,b) is a generic vector in C^2 (a,b) = α (i,0) + β (0,i) and i obtained that α = a/i , β = b/i

I guess i must separate the real part and the complex part

for exaple, a generic vector in C^2 is (a+bi , c+di) so: (a+bi , c+di) = α(i,0) + β(0,i)

[supple island]

correct me if i'm wrong, but i don't think alpha and beta can be complex

the generic vector is also not (a.b), it's (a+bi,c+di)

[crisp pagoda]

Thank you so much

[supple island]

np

[crisp pagoda]

so i guess S = {1+i , 1−i} is a generator of C

[supple island]

1+i is a generator of C

cuz it's (1) (i)

if you write it as if it was in R² it's (1,0) (0,i)

[crisp pagoda]

ahhhh mb, thanks

[supple island]

np, C can be a bit confusing since its dimension=2 but it's written as 1 number

it usually helps me seeing it as if it was R²

[cyan pine]

Can anyone help me with 10th CBSE math?

[tropic lava]

for which arguments a and b the function is differentiable

[left knoll]

dude why do u hate urself

its possible but its not worth the effort

trust me

i havea question on vectors pls help someone

i forgot how to do it so pls dont judge me to harshly

IK ITS EASY SHHH

[cinder yacht]

if you see C^2 as a real vector space (meaning coordinates of vectors in a base are real numbers) then yea, but if you see C^2 as a complex vector space (meaning coordinates of vectors in a base can be complex numbers) then it's 2D

[left knoll]

whats the q

[supple island]

Ah shit i knew there was something wronng about It, i should stop answering Linear algebra questions for now and just tag you instead

[left knoll]

could u answer mine pls?

[supple island]

There's no question thou

[left knoll]

fair poin

its calculate ac and direction of ac

[supple island]

If you consider North East being at 45° it should be quite easy

[left knoll]

ohhh ok cause i was confused that they gave no angle

ty

[cinder yacht]

nahh ur answer was right anyway, just under the assumption that we look at it as a real vector space

[supple island]

oh ok cool

thx fpr the clarification

[astral berry]

any clue in how to think about this question?

[left knoll]

ok so assume look at the given graphs f(x) and g(x)

we know that g(x) is a negative mod graph/absolute value graph

lets just assume for argument sake that f(x) is a parabola

so basically think of the composite function as f(-|x|)

and then u can work the answer out

[zenith dock]

i am at a complete loss here, how can I solve for x?

[cinder yacht]

let f(x) = 1+x/e + x^2/(2 e^2) - 3 exp(-x)
then f'(x) = 1/e + x/e^2 + 3 exp(-x) > 0 (we can prove that it's positive by computing f''(x) and looking at the sign of the global minimum of f' (x))
so f is increasing, so there can't be more than 1 solution

f(0) = 1 - 3 = -2 < 0
f(1) = 1 - 2 exp(-1) + 1/(2 e^2) > 0
so the unique solution is between x=0 and x=1

that's all I know lol

idk how to solve for x either tbh

[zenith dock]

thanks for the help anyway

[left knoll]

is there anyway to solve this except graphically

[left knoll]

why dont u just graph it?

graph each side of the equation and then just intersection point

no?

[zenith dock]

I could but I doubt it'll be a satisfactory answer to the question

[left knoll]

why

[zenith dock]

Cause my teacher is like that

[left knoll]

what does satisfactory answer mean

its math

the answer will be the same

?

so is this ok @zenith dock ?

if not ill try to do it algebraically

[zenith dock]

You can try, I'm not sure how I could graph it

What I meant was that by graphing it you won't get the exact answer

I've checked in wolframalpha is that the answer has infinite decimal places or so, so most likely wolfram just approximated it without getting an exact value because it wasn't able to

[left knoll]

oh exact

give me a sec

do u have the answer

just incase so i can check?

[zenith dock]

I'll calculate it again, one sec

[left knoll]

give me like 5 min

[zenith dock]

https://www.wolframalpha.com/input?i=1+%2B+x%2Fe+%2B+x^2%2F(2e^2)+%3D+3%2Fe^x

[left knoll]

@zenith dock i dont think its possible

r u sure the q is correct?

[zenith dock]

yeah same i've tried like every trick i know

most likely

i can try to translate it to english but it's a statistics question

[left knoll]

did u copy it down correctly?

[zenith dock]

yup, i've got the pdf

[left knoll]

yea go ahead

[zenith dock]

a random variable X has a poisson distribution of the parameter λ. For which values of λ does the probability of X<3 equal 3/e^λ?

rough translation but i think the important bits are correct

so what i did was added the probabilities of X = 0 and X = 1 and X = 2

[left knoll]

yea ok what u did is correct

but i think u also need to consider the values of 2.999999...

[zenith dock]

i'm not sure how to explain this but isn't poisson distribution discrete? so the only X'es that can be used are integers starting from 0

[left knoll]

oh i didnt read that part

my b

hmm ok then what u have done is correct

and its now an algebra problem

[zenith dock]

exactly, that's why i ommited the statistics part cause i was kinda confident that part was done correctly

[left knoll]

yea that part is correct

let me think

[left knoll]

is this meant to say for what values of x?

not lambda

or am i mistaken

[zenith dock]

when I posted the algebra part of the question I substituted lambda for x to make the potential discussion easier

[left knoll]

ok well now im confused

[zenith dock]

ok let me rewrite

i used x instead of λ in this cause im lazy

it should be 1 + λ/e + λ^2/2e^2 = 3/e^λ

have I made myself clear now?

[left knoll]

the formula is f(x)=(lambda x/x!)e^-lambda

yes?

[left knoll]

i think so

[left knoll]

is this correct @zenith dock

its been a while since i have done random variables

[zenith dock]

the possibility of X being equal to some K is λ^k*e^(-λ)/k!

[left knoll]

yea

ok

so we need to find x right?

for which it is equal to the thing u said above

[zenith dock]

we need to find λ

[left knoll]

or k in this case

ahh ok ok

[zenith dock]

P(X<3) = p(x=0) + p(x=1) + p(x=2)

we have the K for all of these three things

[left knoll]

yea thats fine

its still boils down to the fucking algebra

sorry man i dont think i can help you

im going in circles here with the equation

best of luck

[zenith dock]

thanks for the effort anyway

appreciate it, fr

[left knoll]

sorry once again dude

[zenith dock]

no worries

oh wait i think im dumb af and I wrote the equation wrong @left knoll
P(x<3) = p(x=0) + p(x=1) + p(x=2)
which gives us
3/e^λ = λ^0/(0!*e^λ) + λ^1/(1!*e^λ) + λ^2/(2! *e^λ)
we can multiply both sides by e^λ and then it's a simple quadratic equation

λ = 1 or λ = -2 but λ has to be positive in a poisson distribution iirc

[left knoll]

I FUCKING KNEW IT

CAUSE IT WAS COMING CLOSE AS A QUADRATIC

[zenith dock]

lmao

[left knoll]

WELL DONE MAN

[zenith dock]

thank you

[left knoll]

I KNEW I WAS SHIT AT ARITHMETIC

[left knoll]

what for

u did all the heavy lifting

[zenith dock]

for listening to my ramblings and trying to help

[left knoll]

haha np man glad u figured it out

[ember kernel]

@left knoll @zenith dock Hey ! For answers that are 20+ message-long, I suggest you switch to a thread or to dm's next time ;)

[zenith dock]

my bad, sorry!

[silver pier]

can anyone explain how this part was derived

my intuition tells me that this can be done but i cant explain it why it can be done

I think that, I can derive the ratios from the four segmented triangles and all the ratios equal to each other because earlier I proved the corresponding angles of the sides are equal

Idk is this the correct explanation or.not

[dusk stone]

struggling with this, can anyone kindly help

[weary arrow]

If I've understood the question correctly then the total costs per week would be X - 20 + 1000, while the earnings per week would be 50X. Then you find the point where these two functions intercept and the x-value of that point will be the number of trips needed to break even.

[drowsy rose]

Stuck on this simplification if someone would check it for me I’d be super grateful

Mark scheme says:

Why isn’t it this instead:

[supple island]

becaues you like to express everything as e^itheta so that you can represent it with a sinusoidal, but i'd need more context on what you're doing

[solemn ore]

both are correct... depends on what more you want to do with that equation... if simplifying is the only goal, than the first form is correct because when everything is inside of brackets, ist considered more simple.... does that help? do you want further explanation ?

[drowsy rose]

ohhhhh yes of course thanks a ton guys

just me being a bit slow hahaha

tyvm @solemn ore @supple island

[ember kernel]

best answer, although I'd argue that the a+jb form would be considered more simplified than j(b-ja)

[left knoll]

My bad will keep in mind next time

Anyway to solve this except graphically

[ember kernel]

The points are colinear if and only if PQ = a QR (with a = some constant value)

The formula comes from the fact that the points are collinear if two of the three vectors (PQ, QR, RP) have the same direction, no matter their relative norm

the constant "a" acts as the degree of freedom regarding the norms

[left knoll]

Ok ok that makes sense thank you so much

[tribal sable]

how to solve this

and what does the first formula line say

[sullen verge]

it's not really clear what the question is

you need to find x? idk

oh oops i didnt read till the end i guess my bad

[tribal sable]

yeah it asks p/1012 but what does that mean either

[sullen verge]

no idea

sorry😅

[tribal sable]

it is okayy

[timber viper]

Jenny is going to attend a sports camp for 7 days. Each day, she will play exactly one
of three sports: hockey, tennis or camogie. The only restriction is that in any period of 4
consecutive days, she must play all three sports.
Find, with proof, the number of possible sports schedules for Jenny’s week.

[timber viper]

i know how to break it down but i dont know how to calculate it

[timber viper]

@ember kernel I think your tutorial just got deleted for my question

[cinder yacht]

the first formula line says that
E(X) = 1 * P(X=1) + 2 * P(X=2) + 3 * P(X=3) +... +2023 * P(X=2023)
and since all those probabilities are equal to 1/2023 (if u pick a random number between 1 and 2023, the probability u chose 666 is 1/2023)
so
E(X) = 1 * 1/2023 + 2 * 1/2023 +... + 2023 * 1/2023
= 1/2023 * [1 + 2 +... + 2023]
= 1/2023 * [ 2023 * 2024 / 2] using the third formula
= 1012

you do kinda the same with E[X^2] to find that
E[X^2] = 2024 * 4047/6 = 1012 * 4047/3 = 1012 * 1349 (check if i got my mental math right), using the fourth formula
u use the second formula to find that
p = Var(X) = 1012 * 337
meaning p/1012 = 337

[ember kernel]

Yup, because I was answering half-focused, and realised I had misunderstood the question

[timber viper]

haha but thxs for helping anyways !

[cinder yacht]

seems complicated

[timber viper]

this is why i need help haha 🥲

[cinder yacht]

thought abt it for 10 mins, couldn't find a good way :(

[timber viper]

yh probabilities questions are mostly logics questions which is pretty confusing ngl

[cinder yacht]

apart from like making a trees of all possibilities, with some simplifications, I can't think of anythinh

[timber viper]

i think is about combinations hmmm

[cinder yacht]

like in the 4 first days, there must be one sport that appears twice. call that sport A
then call the first sport, other than A, that appears in the 4 first days, sport B
and the other one C
so for first 4 days it's either
AABC
ABAC
BAAC
BACA
BCAA
ABCA
and from each of those, would branch out the trees to add all possible 5th letters, then 6th,then 7th

I think it would be really annoying lol, and there must be a straightforward way

(at the end, gotta multiply the number of 7-letter-words found by 3! to account for the assignments of A, B, C to hockey, tennis, camogie)

[timber viper]

hmm make sense

[timber viper]

i'll think about what u had said. but someone also had lead to before would that be the easier way u r talking about

[cinder yacht]

idk what this means on its own

like this is just part of the answer that person gave you, not the whole answer

[timber viper]

so first i said this than

than

[cinder yacht]

u guys both sound confusing xD

but yea what u wrote abt first three 3 days with one sport each is wrong, it's 3! not 3C1

3 * 2 * 1

and the rest of what you wrote and what he wrote I don't understand it

I'm not sure he understands the answer

[timber viper]

this is what the last thing he told me after telling me about the bookshelf thing

[cinder yacht]

I think ur friend is wrong

[timber viper]

oo really what about his logic

[cinder yacht]

I think he's wrong

[timber viper]

lol XD then ig is a pretty confusing question!

[echo tiger]

help?

Suppose in step 0 we have a line segment 6 units long. Consider the process of dividing this segment into three equal parts and replacing its middle third with a square without the base, as shown in the following figure.

Replace the middle third with a square without the base.

Let the figure Fk be obtained by repeating this process for each of the segments of step k−1, for k≥1.

Determine the step k from which the figure Fk will be at least 576 units long.

[left knoll]

Hi, can someone please explain this one?

[unreal ore]

x^2+7y=-9x〖+y〗^2-3
can u guys turn this into general form?

[drowsy rose]

anyone know how to approach this q?

part c)

[clear belfry]

help pls

solve for x

[mental tapir]

Can anyone help me in solving these questions ?

[ember kernel]

You can prove that X is 2 by 2, because the other two matrices are as well
Start off by defining X := [[a b] [c d]]
Your goal is to find the values of a, b, c and d

Using the formula of matrix multiplication, you can find that
2a + 3c = -5

2b + 3d = -8

etc.

The, you'll be left with four equations of four unknowns (and even better, the system can even be split into two independant sub-systems, one with a and c, the other with b and d)

Just solve the system for a, b, c, d

Another way of finding X would have been to compute the inverse of the matrix [[2 3] [5 9]], and pre-multiply the whole equation by that same inverse (just like you'd solve 9x = 4 by dividing both terms by 9)
The only thing that prevents us from following that method is that the determinant of [[2 3] [5 9]] is 0, and thus it has no inverse

I hope I was able to help you

[clear belfry]

thanks

[ember kernel]

Sorry, the text is barely legible, can't help you ^^

[mental tapir]

Is it visible now ?

[glossy falcon]

Write the polynomial function of the third degree (or lower) whose graph passes through the points P(-2.-9). Q(0, 5), R(1, 6) and S(3,-4)

Guys I really can't solve this 😫

[supple island]

write general polynomial function ax³+bx²+cx+d=y, make a system of 4 equations substituting the points P,Q,R,S

[zenith oyster]

Hi can someone pls help

[unique zinc]

180- (116/2)-(50/2)=97

does anyone know how to solve this? ;-; its matrix but im not even sure what type of question is this

[cinder yacht]

I dont understand the question. Why not just prove that Rx(a) * Rx(b) = Rx(a+b)
and then just set alpha_1 =.. = alpha_N = theta/N?

to prove that Rx(a) * Rx(b) = Rx(a+b) you use 2 trigonometry formulas, each twice
(formulas of cos(a+b), sin(a+b))

[cinder yacht]

idk what kind of theorems you have, but basically it's like u have
an equation Ax=b where A is a 3x4 matrix, x a 4x1 vector and b a 3x1 vector
they gave u two solutions x' and x'' to that equation
so Ax' = b and Ax'' = b
so u can subtract those equations and factor by A :
A(x'' - x') = 0
cool, let us set y = x''-x' = (5, 5, 5, 5) = 5 * (1,1,1,1)
that means 5 A * (1,1, 1,1) = 0
meaning A * (1,1,1,1) = 0
so u can take the equation Ax'=b, and add as many times A(1,1,1,1) as you want on the left side
in x'=(2, 3,4,5), the "x3 coordinate" has value 4, so to reach 24, we add 20 times that A(1,1,1,1)
in other words, :
20 * A(1,1,1,1) + A(2,3,4,5) = 20 * 0 + b
so A(22, 23, 24, 25) = b
so (22,23,24,25) is a solution

now if u didn't study matrices (and how linear equations are basically like Ax=b matrix equations) , it would be more bothersome to explain the solution in msgs

[forest tapir]

you just split it into 4 right triangles and use sin cos tan

actually you can do it without that

[echo tiger]

I really need help guys

Suppose that in the initial step we have a segment 5 units long. Consider the process of dividing the segment into four equal parts and replacing the second and third quarters with equilateral triangles without the base, as shown in the bottom 6-segment figure.

Determine the spatial dimension of the fractal that is obtained by repeating this process indefinitely.
Provide your answer to at least two decimal places.

[forest tapir]

didn't finish it, just for demonstration

get it?

[unique zinc]

we did learn matrix! the reason i was confused was bc it looks like its just adding things together which is very different from what i used to see in matrix problems (we are not solving a matrix or anything like that) but i completely forgot about that Ax=b thing! and now it actually makes sense!! i need to watch more youtube video to get myself used to questions like this haha. thank you so much for such a detailed explaination! it helps a lot!

[mental tapir]

??

[forest tapir]

sorry I don't really get what's asked since i didn't study in english 😬 if I could help I would!!

[left knoll]

do i have to give direction in radians here because thats what the answer did but nowhere is it specified that radians is required

[iron belfry]

angle pya = ypa because ya = pa

50 + 2x = 180
2x = 130

x = 35

jy = jp ==> jyp = jpy

116 + 2a = 180
2a = 180-116
a = 64/2
a= 32

jyp = jpy = 32 + 35 = 67

[zenith oyster]

Thx

[zenith oyster]

Tysm

[iron belfry]

your welcome :)

[minor ledge]

Does anyone know what happens when you have a complex differential equation with both sine and cosine on the right of it? As in y'+5y=sinx+cosx for example

[tardy hedge]

What's wrong in

This

[ember kernel]

Then the particular solution will be a linear combination of a cos and a sine of the same frequency as the ones present in the equation.
That means, here, that y_p(t) = A cos(t) + B sin(t)

But, more generally, keep in mind that the particular solutions of different independant terms can be found independently, and then added together

Example :
y'' -4y'= cos(3t) + 4 exp(2t)

Here, you can find the two particular solutions y_1(t) and y_2(t) such that :
y_1''(t) - 4 y_1'(t) = cos(3t)
y_2''(t) - 4 y_2'(t) = 4 exp(2t)

Then the particular solution of the whole equation will be y_p(t) = y_1(t) + y_2(t)

I hope I was able to help you ^^

[tardy hedge]

Can someone tell what i have done wrong over here

[ember kernel]

Looks pretty fine to me. What makes you say it's wrong ?

[tardy hedge]

Answer given in the book is 1 and not 2. I think it might be a mis print

[ember kernel]

Well, you proved that i + i = 2

Thus i = 1

[tardy hedge]

Ohhh shitt, how did I miss that

Thanks so much mate

[ember kernel]

"Add (1) + (2)"

[tardy hedge]

Can't believe i spent 30 mins on this and couldn't figure that out

[ember kernel]

Yup, that happens.
Last night I spent 3 hours staring at my screen, looking for the cause of a bug in my code. Turns out I had mistyped one letter

So yeah, that happens

[tardy hedge]

Hahaha, sigh

[minor ledge]

Thanks ^-^

[leaden geode]

given that 1<n<2 state a value for n which n^2 > 1
is it 2?

like the minimum even tho it doesnt say

[forest tapir]

but n needs to be smaller than 2 so it can't be 2

[fervent dagger]

simplify it with steps pls. Im not able to find e
e = √[1 + (64/e²) / (256/e⁴)]

[ember kernel]

x^2 > 1 for any real value x>1

[ember kernel]

• 256 = 16^2
• e^4 = (e²)^2
• sqrt(x²) = x if x >= 0
• sqrt(a/b) = sqrt(a)/sqrt(b) if a and b are positive

Now you've got enough info

[fervent dagger]

Oh thank you

[left knoll]

any takers?

would be much appreciated

[ember kernel]

I don't know if that'll lead to the answer but have you tried splitting into simple fractions ?

[left knoll]

yea got nowhere

[ember kernel]

The answer appears to be pi/4

[supple island]

this should be the obvious method but there's probably a smarter one, since you can't write a polynomial of degree 2015

[left knoll]

Can either of you help me with the working im more interested in that than the final answer @ember kernel @supple island

[ember kernel]

Nope sry I'm super busy

Thanks for offering though

[left knoll]

Oh sorry sorry my b

[left knoll]

Haha lmao np man if u get a chance i would greatly appreciate it

[karmic scaffold]

how?

[supple island]

a is a real constant, any ideas?

[delicate cave]

flammable math had a video on a similar question

https://www.youtube.com/watch?v=YWBdwYr6PGg

[supple island]

haven't seen the video, but maybe if i express the cosx as (e^ix+e^-ix)/2 it's actually similar to a fourier transform

oh ok easier than i thought

the answer i got is pi/4a (e^a+e^-a)

[haughty belfry]

A single light bulb hanging from a ceiling in a room shines on an object on a table and casts
a shadow on one of the room’s walls. If the light’s position is p = (5, 3, 10) and the normal to
the wall is given by n = (1, −1, 2)T verify that a vertex q = (2, 3, 4) of the object on the table
create a shadow at the point r = (1, 3, 2) on the wall. anyone know how to approach this question? any help would be appreciated.

[rustic shuttle]

15! /3!4!8!
if it is like this it should be 225225

[ember kernel]

Hi ! Did someone ping me ?

[vapid spruce]

can someone tell how to do the 1st ques?

[halcyon parrot]

help 🥲

[delicate cave]

with a fixed perimeter, maximum area is of a circle
2 PI R = 242
find PI R^2

[vapid spruce]

What is Tn here?

[iron belfry]

formula of nth term

[vapid spruce]

N term?

Oh icic

[iron belfry]

or i think you have learnt it as An or smth

[vapid spruce]

Yea yea

[iron belfry]

i am also in class 10 cbse lol

[vapid spruce]

You also have exam on 5 then?

[iron belfry]

yes , but the sad thing is i have my 2nd language exam right after maths the next day :(

[vapid spruce]

Btw thanks dude

All the best to you too

[iron belfry]

thanks and all the best

[vapid spruce]

Btw thx for the sol too

[tardy hedge]

It can also be written as y = 1+Ae^-x where A=(-C') right?

[tardy hedge]

General solution is needed

[heady tree]

what would be the roots of this in polar form?

[ember kernel]

Maybe you should convert z³ to its polar form first

Then apply the formula you've surely learnt about

[heady tree]

yeah i've gotten to 13cis(2pi/3) and then substituted that into the nth roots formula but i think my error is cropping up in ensuring that my resultant answers satisfy -pi<= Arg(z) <= pi

[heady tree]

never mind, i've figured it out, thanks

[random flame]

Hey can someone help me with the last line? I’m not sure how to differentiate this. Ping if you do help and thanks in advance!!

[ember kernel]

Apply the chain rule :

1. Differentiate the ln, that gives 1/(...)
2. Differentiate the content of the ln (what I denoted as (...)). It's a fraction of functions so there is a specific formula to use

Multiply (1) by (2) ('cause chain rule) and you're done

[random flame]

Ah thank you !!

[sullen verge]

it's probably a long shot but any of you is completing the bachelor of science at l'X?

[delicate cave]

what's that ?

[sullen verge]

it's a bachelor program (maths and a specialty in cs physics or economics) at Polytechnique Paris

[round belfry]

aka the best engineer school in france x)

[cinder yacht]

ens Ulm is better than us at science tho

[zinc nimbus]

can someone pls tell me what do I type to make this into a number

[forest tapir]

are you sure your calculator gives you the whole number? cause mine doesn't either

i guess it depends on the calculator

[zinc nimbus]

let me try a small number

[forest tapir]

okk

[zinc nimbus]

u were right

[forest tapir]

hhaha ok so problem solved?

[zinc nimbus]

yes thanks so much

[forest tapir]

okayy np 🤗

[untold shard]

does anyone know how logarithmic properties were developed?

[ember kernel]

Several different mathematicians worked on logarithms. Is there a specific property you're talking about ?

[sullen verge]

do you go there?

[supple island]

don't post memes here

[dreamy ember]

hi can anyone explain this solution to me?

i dont get the A3 part

Nvm got it

[untold shard]

found it , thanks

[round belfry]

yeah probably

[round belfry]

no sorry

[untold shard]

can this exits ?

[delicate cave]

we generally do not take negative bases in a logarithm

however logically speaking, there is nothing wrong in what you've done

[hearty jackal]

is anyone adept at wolfram mathematica software?

[supple island]

no, logarithms can't have a negative base

[ember kernel]

Completing what everyone said.
Although (-2)^3 = -8 is valid, the log operator is only defined for strictly positive bases, so what you wrote is rigorously wrong

[cinder yacht]

completing what everyone said
the underlying reason we require the log operator to have a positive base is that we want it to be applicable to real numbers, not necessarily integer numbers.
for example we want log_A(6.6666) to make sense. if we allow the base, A, to be negative, then it doesn't make sense (what's (-3)^1.5 for example?)

we don't have much to gain by extending the definition to negative bases (it only helps us find integers x such that A^x = n, where A and n are (possibly negative) integers). However we have a lot to lose (wouldn't be able to apply the log operator to non-integer numbers anymore)

[left knoll]

yo lads

i have no idea whats going on with part c

i'd really appreciate it if u guys would help me with this

where u get 133 from first of all

[hollow blade]

hey, i am working on probability now so i can't walk you through it 100% (because I am still figuring it out myself), but as described in the problem you can see it is normal distribution and it is asking for conditional probability (we know this because their language "Given that..."). So, knowing Alice is going on a 6 hour journey, and she hasn't charged phone in 127 hours, they do 6+127 which is 133. So pretty much they are asking you: what is the probability the phone will work for longer than 133 hours GIVEN THAT she hasn't charged it in 127 hours?

and from there they apply the formula for the conditional probability and solves... hopefully this helped clear the problem a bit for you?

[left knoll]

yeah thank you

one more thing

the line where it says 1-0.9861 what happened there

[hollow blade]

I am not completely sure, maybe wait until someone else answers this for you. My guess would be they evaluate P(L>133) by finding P(L<133), which is 0.9861 and then use 1-0.9861 which would be calculating for the complement, or everything besides P(L<133), which would be P(L>133). Think of it as if: you cannot calculate all possibilities because there is no top limit (L could hypothetically go infinitely), so you take the inverse of what you don't want. They then do that for both sides, because they are both >, then solves for the answer. That's my best guess because I am learning this at the same time as you :D

I found a link that may help you further: https://math.stackexchange.com/questions/126155/normal-distribution-and-conditional-probability

[left knoll]

bruh this dr frost don is making it more complicated

all u do is normal cd on calc and done

thank you brother

i have something to tell u bro @hollow blade

tell me when u ready

[hollow blade]

what's up?

[left knoll]

ello mota junaibh

aap ke kya khaal heh

[untold shard]

thanks for all the answers , ig the properties don't work if we take negative numbers although we can use complex numbers but anyways , discord is so useful man !

[mild bloom]

hey guys ive got a math test in a few weeks

can someone help me with a question?

15 = x + 5

find x

pls help fast

[cunning mural]

erm selpo its 10

[mild bloom]

are you sure my mum said it was 5

[cunning mural]

yes i did some napkin math

[cosmic viper]

Subtract 5 from both sides than you’re left with 10=x
Example:
15=x+5
15-5=x+5-5
10=x
Whatever you do to one side of the equation you have to do to the other.

[left knoll]

i got up to cos-1(-1/2)

but what quadrant is theta in?

2nd or third

[left knoll]

cos^-1(-1/2)= pi - cos^-1(1/2)
= pi - cos^-1(cos pi/3)
=pi - pi/3
=(2/3)pi

[left knoll]

ye ik how to work it out

why is it the second quadrant tho

why not third????

[left knoll]

https://mathmistakes.info/facts/TrigFacts/learn/uc/nar.html
this might help

ok ok i dont think im conveying my point

i know how to use the diagram and everything

my question is

cos-1(-1/2)=theta

theta has two solutions

yes?

i think theta has only one solution

[left knoll]

?

how

cos is negative in both second and third quad

yes

ok

andddddd

thus two solutions

my question is for the vector question the answer only considered the 2nd quad not third

why is that the case

oh got it

ye

do u know why?

oh also maybe we should create a seperate thread for this

because its a lot of messages and i dont want to ruin the flow for the chat

[ember kernel]

Ok be careful there.

There are two kinds of logarithms.
One is defined for strictly positive real numbers.
The other is defined for all complex numbers except 0

They are very different, and the latter uses the former in its formula.

Your mistake:
The complex logarithms doesn't take any base. We just write log(z), because log_w(z) makes absolutely no sense.

The real logarithm, however, does need a base to work, and is written as log_a(x) or ln(x), but rigorously not log(x) (sometimes people write it that way, but it implicitly means log_10(x) or log_e(x))

The one you showed us contained a base, so that means you were talking about the real logarithm, not the complex one

In that case negative numbers are forbidden

In the complex logarithm, any complex numbers that isn't 0 is accepted

I hope this helped you understand the difference between the two kinds of log

[untold shard]

yeah for sure

[left knoll]

bwhahahahah so good thx

ill remember that

[cloud night]

Hello can anyone help me with part b of this question?

Cuz after I wrote this I'm clueless as hell

[cinder yacht]

A^(k+1)
= A^k * A
= [ (2^k - 1) A - (2^k - 2) I ] A
= (2^k - 1) A² - (2^k - 2) A
now we use from question a that A² = 3A - 2I
so A^(k+1)
= (2^k - 1) * (3A-2I) - (2^k - 2) A
= (3 * 2^k - 3 * 1 - 2^k + 2) A - (2^k - 1) * 2 I
= ( 2 * 2^k - 1 ) A - (2^(k+1) - 2) * I
= (2^(k+1) - 1) A - (2^(k+1) - 2) * I

[left knoll]

Can someone please help me with this ?

[thin verge]

All of them?

[left knoll]

It would be better if all but don't have to !!
Question 6 is the hardest one for me

[ember kernel]

Can someone please help me with this

[ember kernel]

Hey ! I created a thread that, hopefully, will help you understand how it is possible to work your way around that kind of problems using units

It could also be useful to anyone that's struggling with memorizing/using high school physics formulas

[left knoll]

I'm having trouble with definite integration (calculus btw)
So I wrote down this example that's done already but I have no idea what I'm seeing so if anyone can explain the steps I'd appreciate it

[cloud night]

thanks !

[left knoll]

ok so u r confused about the steps?

as in the method of solving these kinds of questions

[left knoll]

yeah

[left knoll]

ok so the method u r using here is called u substitution

now instead of me doing a poor job on explaining how to do this i suggest having a look at this

https://www.youtube.com/watch?v=8B31SAk1nD8&t=331s

it explains it really well

if you are still confused then i can try to help

[left knoll]

thank you!

[dusk stone]

had hard time solving this one, any help would be appreciated

[void pewter]

I have to take my final for quantitative reasoning and have not paid attention all year and need help lol

[ember kernel]

Quick solution, just get better ✌️

[supple island]

git gud

[left knoll]

Hi I'm trying to get the right volume for a cylinder and I used the right formula and everything but I don't know why I got 6438.7 instead of 650.617??? I don't know what I'm doing wrong

[forest tapir]

i get the same answer...

@left knoll

not exactly, i get 6438.87 but doesn't really matter hahaha

[forest tapir]

i guess since there's nothing wrong with the formula or the numbers maybe you copied the diameter and height wrong? if not then it has to be the solution that's wrong

[forest tapir]

i don't really get this...by unit they mean department plus assembly right? but if we have 18 hours for assembly then there's only 3 hours for department left. so how are we supposed to produce anything if we run out of time for the department but still have 15 hours left for assembly, when assembly takes less time

[forest tapir]

idk if i understood it correctly hahaha pls explain if i'm wrong

[forest tapir]

i think it's (x,-y)

@left knoll

[fathom tartan]

Hey,i just want tips on how to memorize the TSA , CSA AND volumes of shapes , i have my exams in some days but I'm not able to memorize these thing . Pls help .

[left knoll]

ah i got used circumference instead of diameter- lol i fixed it

[vague dagger]

any math helper here

need some help rn

[delicate cave]

if its a question, post it here

[vague dagger]

oh im good now , thanks!

[hidden skiff]

With limited time I would just recommend making an Anki deck of the formulas you want to memorize and overstudy until your exam. When you review each card read the formula out loud e.g. "A sphere's volume is four-thirds of pi times the radius cubed", I find this helps it stick in my memory. For each formula say it the same way every time and try to keep the same rhythm/cadence in your voice. Your brain will cling to the words and rhythm better than it will the image of the symbols.

[fathom tartan]

Thanks a lot for your advice , i will try this method for sure.

[cinder yacht]

ye

[burnt quail]

how do u get this?

[astral furnace]

Simple maths

[burnt quail]

yeah i need explanation not ranting

i get 6.45....

[burnt quail]

sooo

[astral furnace]

BRUH

[rustic shuttle]

probably he wasn't multiplying by Pi

[burnt quail]

pi is infinite

ok nvm

im dumb

[astral furnace]

BRUH

I'm literally a doctor , Haven studied maths since 4 years

😂

[delicate cave]

😂

[atomic dagger]

hi ! i'm a little confused when solving trigonometric equations, how do I know what to add after the solution (+kpi, +2kpi, +kpi/2)? Sometimes it feels like I can only know if I already have the solution memorized and know at what intervals we obtain the solution. For example:
cos(x) = 1/2 has as solution
x= pi/3 + 2k*pi or x = -pi/3 +2kpi
but tan(x) = 1 is x = pi/4 + kpi
sin(x) = 0, x = kpi

How do I know when calculating whether to add 2kpi, kpi etc... ?

[atomic dagger]

thank you so much i'd never seen this before!

[viral bluff]

The measure of the supplement of angle A is 40 degrees larger than twice the measure of the complement of angle A. What is the sum in degrees, of the measures of the supplement and complement of angle A?

I forgot how to do this

[supple island]

180-A=40+2(90-A)

supplement is the angle that adds up to 180, complement to 90

[viral bluff]

thx alot

[left knoll]

hi

where did the 2 come from in the first line of working out

i understand the -4

[left knoll]

is this even correct or what i cant see it

[hidden skiff]

It could be a typo since (4 sin 30)j = 2j, which is what it simplifies to on the second line

[left knoll]

thank you brother

[left knoll]

hey

why is it -2T in the 2nd marking point

is it not being projected upwards?

[rustic shuttle]

Yes, it would be 2t-(1/2)gt² but the whole equation is multiplied by (-1) so it becomes -2t + (1/2)gt²

[knotty sky]

if i have an inequality: x^2>= 1 then can i write it as x>=1 by taking square root on both sides

[ember kernel]

No, you can't

The first inequality has ]-inf,-1]U[1,inf[ as solutions.
The second inequality only has [1, inf[

Different solutions means the inequalities aren't equivalent, and thus that you made a mistake somewhere

The actual answer is
x² >= 1 is equivalent to "x>= 1 or x <= -1"

Just like in classic equations, taking the sqrt of both sides will always introduce a +- factor

Inequalities aren't exceptions to that. Furthermore : the - factor also causes the >= to switch direction and become <=

[knotty sky]

Ohhhh..... i get it now
Thank you so much!!

[lapis relic]

<@&942391219206647828>

[grave elbow]

help, i'm so confused

[rustic shuttle]

The "??" should be points from the circles, as it is written it's not possible to solve this

[grave elbow]

i thought so as well

this was the answer but i dont get it

[rustic shuttle]

AC is a diameter of the larger circle and BC is a chord in the larger circle and is tangent to the smaller circle. AB has length 140.
This way you should be able to solve, if u still can't do it i can help

[grave elbow]

could you draw out the diagram so i can understand? 🥲

[rustic shuttle]

@grave elbow

[low oriole]

1. An officer on an 90 ft. observation tower measures the angle of depression of a boat to be 59°. How far is the boat from the tower? (Express your answer to the nearest whole number)

2. From the top of the house that is 35 m high, the angle of depression of a car on the ground is observed to be 25°. Find the distance of the car from the base of the house. (Express your answer to the nearest whole number)

[forest tapir]

@low oriole

OH WAIT

That's not the angle of depression right?

[low oriole]

it is

[forest tapir]

oh really? okayyy i wasn't sure

[low oriole]

yes xd

[forest tapir]

i didn't calculate it i think you can do that right?

[low oriole]

yes! but what does "/.90" this mean?? it wasn't taught yet......

[forest tapir]

oh hahahaha

sorry it just means that you multiply everything with 90 so that you get x

or with 35

[low oriole]

ohhhh i see

[forest tapir]

you basically bring it to the other side so that you have numbers on one side and variables on the other

[low oriole]

thank youuu so muchhh actually i already answered it but mines wrong

[forest tapir]

ohh hahaha no problemm😊

[forest tapir]

what part was wrong?

[low oriole]

everyhting ig TT

1. 54 ft
2. 75 m
   these were my answers

[forest tapir]

ohh🥲

hope it's correct now!!

good to make mistakes and learn from them~

[low oriole]

yes 💓

is the first item 35?? sorry i just wanted to make sure 🥲

im sorry but can i ask somth about the angle of depression im so confused actually my friend sent me a reference link on how to get the answer

she told me to use option 2

so the answer i got is diff to so im so confused

[grave elbow]

help please 🥲

[forest tapir]

what do you mean by item?

[low oriole]

oh its the first ques

[forest tapir]

OHH

yeah so the angle of depression was somehing esle

i wasn't sure cause english isn't my native language hahaha

ok but it's still the same concept

wait let me show you

@low oriole

i always use this method with the Z

if you have two parallel lines that are connected in this Z shape then the two angles are the same

in this case you can see a Z shape too which i coloured in blue here

[forest tapir]

this explains it as well

[forest tapir]

yeah isn't the house 35m high?

[low oriole]

yes

thank you i was confused really...... sorry for disrupting your time btw 🥲😢

[supple island]

if we call X=AB and x=EF, the area of the trapezium is (X+x)(X-x)/2=(X²-x²)/2=35
now we know that BF=sqrt((X-x)²+(X-x)²)=(X-x)sqrt(2)=10 so x=X-10/sqrt(2)

from this you should be able to do everything

[grave elbow]

the answer was 6√2 but i don't get how

[forest tapir]

did you get everything now?

[forest tapir]

also pls don't be sorryyy i really like helping wherever i can

it's better to ask more than not ask

[low oriole]

yes!

[forest tapir]

okayy😊 it should be correct now...if not then tell me, i'll try again hahaha

[static fractal]

❤️

wbb ❤️

[pastel fog]

anyone help me, please

[left knoll]

Let the sides of ABCD be a and sides of EFGD be x then proceed with the following:

[grave elbow]

AAA THANK YOU SO MUCH

that's the right answer, ah finally

[left knoll]

You're welcome:)

[ember kernel]

You know what a gradient is ? If so, then the top of the mountain is located at a local maximum, that is where the gradient is equal to (0, 0)

[pastel fog]

I solved it by myself. thank you for your time and help ❤️

[shell crow]

Hi guys does anyone know how to solve for the domain in this equation? I can solve for polynomials with degree 2 but idk how to solve equations that has more than power 2. Help pls t-t

[frosty moon]

anyone in here thats doing math 3? (11th grade math)

please dm or @ me

[karmic whale]

Find the area bounded by the x-axis and the graph of f(x) = x^23 if -1 ≤x≤1.

[untold shard]

can someone fascinate me more about π

[supple island]

use z=x², then solve for z

[meager sleet]

could someone explain how they got the answer of -2

[summer flare]

5-3x > 11 |-5
-3x > 6 | /3
-x > 2 |+x |-2
x < -2

[meager sleet]

oh my thank you so much

i get it now

[ornate ravine]

I have to end up with an answer like: x = ...

[supple island]

i can give you the answer but this is very basic, you should check the theory again before jumping into exercises

[ornate ravine]

I already did, I know what i have to do, but im not sure which number i have to start with

'+4 or +x', thats my issue :')

[supple island]

the order doesn't matter

as long as you end up with x=

[ornate ravine]

o

okay so i started with uh

5x - 4 = -x - 4
+x
6x - 4 = ?

[delicate cave]

breh 😭

6x - 4 = -4
x = 0

[ornate ravine]

6x : 6 = x
how did u get 0 💀

• 4 : 6

oh wait

oops i forgot half of it

5x - 4 = -x - 4
+x
6x - 4 = -4

6x - 4 = -4
+4
6x

UR RIGHT

I UNDERSTAND OML THIS TOOK ME YEARS

[sullen verge]

any maths book recommendations? i want to start reading maths book but idk how

[turbid jolt]

topic?

[sullen verge]

any topic but im mostly intersted in mathematics that relate to computer science

[turbid jolt]

not too much math, more algorithms, pretty basic, still good. Dont know your level.

[left knoll]

Can someone pls help me with this. I don’t know how to interpret the question in a correct way

[supple island]

what's to interpret? the request is quite straightforward

[left knoll]

I just don’t know how to solve it

I always come the wrong answer so I guessed I’m missing something or misinterpreted

[supple island]

which one? the graph is quite simple

[left knoll]

I can’t make the prescription.

And I’m asking help bc I don’t understand it. Can you pls help me instead of judging the whole time that it’s simple easy. I know for a physics student it probably is and for others maybe too. But I’m not understanding it.

And for me it’s not always that simple

[left knoll]

i need to use this

to prove these two

any help would be greatly appreciated.

[low oriole]

there are multiple answers btw.....

[supple island]

i'm not judging, i just don't understand what you don't get, the problem asks you to do a graph v-t and tells you how the speed changes during time.
you'll have 3 sections, one where's accelerating, one where it's decelerating and another in which the speed is constant

just as the problem says

[supple island]

you just need to substitute lambda u and u+v instead of u in the equation above

[untold shard]

does anyone prepare for imo ?

[left knoll]

ty!

[sand bone]

would this be considered normal distribution or not?

[hidden skiff]

If the data is actually linear then it is possible, but unlikely. It could be that you have not got enough samples to see the full variance of the data, however, if you tried to replicate this by sampling from a normal distribution (the same number of samples as you have data points in your plot) and adding these samples to a line, you would have to do this many times before you saw something that looked anything like this. Of course, it is possible that your data is not actually linear, in which case it would also be possible (and more likely) for the errors in this data to have come from a normal distribution. At any rate, my opinion is that it is very difficult to tell from this plot.

[sand bone]

oh i see, thank you so much for your answer! :))

[forest tapir]

i tried doing 2) and i got 167,5m...seems wrong tho hahahah. what's the solution?

[rustic shuttle]

from what i understood the velocity graph would be something like this

[forest tapir]

uhmm how do i know where the 90° angle is?😭

[forest tapir]

wait i did it again and got 212m

[rustic shuttle]

why would it have a 90º angle?

[forest tapir]

cause they're using sin cos and tan here

[rustic shuttle]

but the triangle doesn't need to have 90º necessarily

[forest tapir]

but then how do you know where the hypotenuse is

[rustic shuttle]

It's not necessarily a right-angled triangle

The triangle could be formed by 3 60º angles

[forest tapir]

ooooooooohh yeah i get it

[forest tapir]

first one is correct

[sullen verge]

thank you so much!

[forest tapir]

@low oriole

[low oriole]

thank you so much!

[forest tapir]

if you need the others too i can try solving them as well

[low oriole]

really? then i would appreciate it!

[forest tapir]

hahah yes i always only do part of it cause i want you to try it on your own too but if you need help with it i can try too

[low oriole]

oh btw the choices in letter b was incorrect i type b instead of c

[forest tapir]

wait wdym i don't get it

[low oriole]

oh i would like to try on my own to buy i don't know how........ all ive known is that a/sin(A)=b/sin(B)=c/sin(C)

[low oriole]

oh sorry hahahah
but the letter b.. i typed the wrong one so i corrected it

[forest tapir]

oh yeah that's basically all you need to know!

i tried showing how i got to the solution a bit but i guess that didn't really explain it hahaha

you know how to solve equations with variables right

so that's all you need to do here

[low oriole]

yes??

[forest tapir]

you can see BC = a

so instead of a you write BC and so on

[low oriole]

ahh okayy i get it nowww

[forest tapir]

reallyy

[low oriole]

yes the illustration

[forest tapir]

yess! and then you use this formula

[low oriole]

ohhhh i seee ill try it

[forest tapir]

i'm trying b) rn too but this one seems kinda difficult

or it's incorrect

[low oriole]

yesss it seems so

[delicate cave]

it is incorrect

its basically the LAW OF SINES

[forest tapir]

ok good hahah i wanna be sure

[low oriole]

i figureed it out! the answer is the1st and last

letter d is ab/sin(c) i typed it wrong TT

[forest tapir]

bruh HAHAH

i just wanted to say i think d) has to be right cause it's always the most complicated ones that are right but AB/sinA doesn't work

[forest tapir]

but yeah this works hahaha

how did you solve c) tho? i gave up on that one

i mean i solved it by using numbers instead of variables but how do you do it without numbers?

[low oriole]

oh the sequence i think it needs to be in order

[soft plover]

Anyone can explain this?

[sullen kettle]

Does that help?

[soft plover]

It helps thank you.

[left knoll]

is there any other logic to this question except 2 to the right and one up

because i would like to see this question from another perspective

[supple island]

it's actually (1 2)

[left knoll]

Could you elaborate @supple island

[supple island]

y=2x means that the vector isn't (2 1) but (1 2)

[left knoll]

ok?

[ember kernel]

Let B = (6, 7) and M = (4, 8)
Let A = (a, b) be the reflection of B with respect to the line y=2x

By symmetry, you know that the vectors A-M = -(B-M) = M-B
Therefore, A = 2M-B = 2(4, 8) - (6, 7) = (2, 9)

Hope you like this solution

Alternatively, you can also say that A-B = 2*(M-B), but that leads to the same final formula A = 2M-B

[fickle mesa]

Help me please evaluate the given problem.

[soft plover]

Anyone know how to do this question?

[median grotto]

Ho many numbers do we have which are 5-digit, and are divisible by 15 and 18?

I've got 9k but im not sure

[ember kernel]

Is this a Laplace transform ?

[left knoll]

yes i very much do tysm!

[rustic shuttle]

1,000

[median grotto]

I mean in Summary

All divided by 15 and 18

[rustic shuttle]

By 15 and 18 is 1000, do you mean "by 15 or 18"?

[median grotto]

Oh yea. Exactly

[rustic shuttle]

I think it would be 10,000 then, divisible by 15 or 18

[fickle mesa]

Yes it is.

[left knoll]

i feel like im being dumb

oh i have to use vectors

[prime pulsar]

looks like cos rule

draw a sketch

then use trig to calculate the angle and length you need

[haughty tangle]

has someone here ever done a generalized mixed effects model with gamma distribution in r?

[blissful ridge]

13q - (12+10q) = 5 (9-q) + 5q

can someone help me

i'm not allowed to use a gymnasium calculater i need to use a simple one from highschool

pls

[rustic shuttle]

13q -12 - 10q = 5*9 - 5q + 5q
13q - 10q = 45+12
3q = 57
q = 57/3 =19

[blissful ridge]

thank you it has been 3 years since i did math the last time i need to refresh a bit thank you

[fickle mesa]

@ember kernel Can you please help me solve this problem.

[ember kernel]

Are u0 and u1 constant ?

'cause if so use these transforms and the linear property of Laplace Transform :

[fickle mesa]

@ember kernel I don't so, I think it needs to be solved using the unit step function approach.

[ember kernel]

I still need to know what u0 and u1 are

[fickle mesa]

The only thing I know is that they are not constants. The question was just given like that.

[ember kernel]

Maybe some abbrevation for u(t) and u(t-1) ?

[fickle mesa]

I think so.

Can you maybe solve using those abbreviation please.

[ember kernel]

Ok so yeah this indeed was an abbreviation I didn't know of

Btw, I'm just googling and looking through Laplace transform tables rn, so anything I'm doing, you can do too

https://tutorial.math.lamar.edu/classes/de/Laplace_Table.aspx

Use the transforms at lines 25 and 30, and I think that should be enough

Good luck

If you need further explanations don't hesitate

[fickle mesa]

Ook,Thank you.😌

[carmine basin]

pls help

[ember kernel]

2^(-4) = (2^4)^(-1)

that's all I'm gonna say

[carmine basin]

ayt denks

[clever karma]

can someone help me with this problem :' )

[ember kernel]

1. Calculate the expression of f(x) using its roots and the y-value of its vertex
2. Calculate the position of the vertex I
3. Let g(x) = ax³ + bx² + cx + d. Build yourself a system of equations knowing that :

• g(I) = f(I)
• g'(-1) = 0
• g'(2) = 0
• g''(I) = 0 (because I is also the x-value located exactly between the two vertices of g)

4. Find all the x-values where f(x) and g(x) intercept, and note keep the two positive ones (because have a closer look at the graph in the question)

5. Integrate f(x)-g(x) between these two positive intersection x-values

And then you're done :)

[clever karma]

is it true that f(x) = g'(x)? because f(x) passin through 2 extrema of g(x)

[prime pulsar]

thats crazey

but maybe
f(x) = k g'(x)

idk if you know that its exactly equal?

[clever karma]

i was thinking of using vietas theorem... but stuck

[prime pulsar]

yes sus them giving us the product of the roots

[prime pulsar]

maybe add that as one of the eqs in the system ^

[ember kernel]

Definitely not

Because that's just a guess, not a fact

[prime pulsar]

wdym

nvm isee the system is for the actual eq and this is for the cubic whos roots represent the intersections

so thyere different coefficients lol

[ember kernel]

Oh yeah

I thought you were talking about the f(x) = g'(x) guess

Although the equality f(x) = k g'(x) + d is indeed true in this scenario, I would recommend to not rely too much on that property, and just follow the general solution I gave

[clever karma]

thanks yall :3 appreciate it

[clever karma]

i have another problem... can you guys help me out 😰 (sorry for my bad english)

[prime pulsar]

oh yeh forgot the +d 😔

[cinder yacht]

there would be no +d here, when f'(x) = 0 we have g(x) = 0
(but generally there's no proof that f'(x) = g(x) here, except by finding the expression of g(x) through solving the equations he mentioned)

[left knoll]

i must be trippin

tell me this aint a mistake

mr quentin

@ember kernel

drop ur wisdom for me brother

[lofty arch]

They’ve subbed in B=-1

[random flame]

Hey can someone help with Q5? My point A is exactly the same as origin so I’m pretty lost- Ping if ya helped and big thank ^^

[hearty jackal]

can you rephrase the question pls?

what is your problem

[wraith pagoda]

where does the "du=-2xdx" and "1/2du=xdx come in solving:

[rustic shuttle]

Do you know how to integrate using substitution?

[wraith pagoda]

like u-substitution? Yeah

[rustic shuttle]

in this case u=9-x^2,
so du=-2xdx or du/2 = -xdx

[zenith dock]

i got a statistics question:
A random variable X has an exponential distribution with a deviation of 1/4. calculate the probability p(|X - EX| > EX^2)

[random flame]

Er the question is already there in the pic

[rare mortar]

i want ask🖐️

what is f(x)?

although teacher teach in class but i not understand

[cunning echo]

value of the function f with input x

[ember kernel]

I suggest you look it up on YouTube, you might find a video that'll explain it way better than us. Just type "what is a function"

[twilit beacon]

Hi , I have a question related to the probabilities. I have a lock of 4 entries and I know the first entry is 3 , how many combinations can I form with it?

i'm not really sure it is 10!/6! (m! /(m-n)! )

[cinder yacht]

so you just need to find the number of combinations u can get with the 3 later entries. That's m^n with m = 10 and n = 3

[twilit beacon]

so , i do not count the first one and I just calculate the total of combining 3 ?

[cinder yacht]

another way to think of it is that this lock will be a number from 3000 to 3999 (included). There are 1000 numbers there
that's the same as 10^3

[cinder yacht]

ye

that formula u wrote is when digits can't be repeated. When there is no repetition, then it's m! / (m-n)!. Here there can be repetition of digits (like 3222 is an okay combination), so it's m^n

[twilit beacon]

ah... I understand , the same thing applies if I know first digit and last one?

[cinder yacht]

if u know first digit and last one, that means u can only choose the 2 middle digits. There are 10^2 combinations then

[twilit beacon]

the thing is I get a really high probability if I divide my number by this

[cinder yacht]

no idea what you mean

[twilit beacon]

would you mind if i dm my question?

[cinder yacht]

id rather u write here

[twilit beacon]

so , 4 digit combinations , we know we cant repeat the digit (ex 4444) also it cant be (1234) , I know the first digit , what's the probability of guessing

[cinder yacht]

ok u didn't say anywhere else that we can't repeat the digit, I understand more now

and what's the first digit

[twilit beacon]

I do 11010*10 - (nr times it repeats 10) -(14 times it is asce/discending) / 10^3 it gives 0.997 and something

5

[cinder yacht]

so why do you say "it can't be 1234" if the first digit is 5 anyway

it won't be 1234 since the first digit is 5

[cunning echo]

yea

[twilit beacon]

a little bit of oopsie in explaining it should be -1 (repeating ) -2 (ascending /discending)

[cinder yacht]

?

you mean it cant' be repeating. And the 4 numbers can't be successive (whether ascending or descending)?

So is 1235 fine?

[twilit beacon]

yes

[cinder yacht]

ok so the number of possible combinations, if we allow ascending and descending combinations :
-Choosing the first digit : only 1 choice (the digit 5)
-Choosing the second : 9 choices (all digits but 5)
-Choosing the third digit : 8 choices (all digits but the 1st and the 2nd)
-Choosing the fourth digit : 7 choices (all digits but the 1st, 2nd and 3rd)
meaning it's 9! / (9-3)! = 504 if you want.
Now that INCLUDES ascending and descending combinations with successive digits. We need to take them off. There are only 2 possible ascending and descending combinations : 5678 and 5432. So it's actually 504 - 2 = 502

that's the number of possible combinations, you're gonna guess one of them. So your probability of guessing right is 1/502

[twilit beacon]

I'm sorry ;-; Ivam a very bad explainer : we can't a combination like (5555) but 5551 should be fine

[cinder yacht]

ah..

[twilit beacon]

I did like this 1* 10 * 10 * 10 - 1 - 2 but I'm not sure with what to divide

I divided by 10!/6!

[cinder yacht]

so 10^3
minus 1 (the choice 5555)
minus 2 (the choices 5678 and 5432)

that's 997 possible combinations

and if you guess randomly one of those 997 possible combinations, then ur probability that your guess is right is 1/997

[twilit beacon]

oh...

[cinder yacht]

no idea why you're dividing by 10!/6!

[twilit beacon]

damn ... I get it

thank you for patience and help ^^!

[cinder yacht]

don't worry!

[left knoll]

i am so stupid

me rn

[olive trail]

Hi. Could anyone please help me with 33?

[edgy orbit]

You have to put t= f(x) and replace t in y(t). Then I suggest you draw y(x) to understand what it looks like

Then integrate

[feral warren]

need help asap

thanks!

[little mesa]

Hint: to find tangents you will need to use differentiate.

[subtle sluice]

i love you too

[delicate cave]

love you too!!